polls_2008 %>% select(start_date, Obama, McCain)

Source: local data frame [543 x 3]

   start_date Obama McCain
       (time) (dbl)  (dbl)
1  2008-11-03  0.52   0.43
2  2008-11-02  0.49   0.44
3  2008-11-01  0.51   0.46
4  2008-11-01  0.52   0.44
5  2008-11-01  0.52   0.46
6  2008-11-01  0.53   0.45
7  2008-10-31  0.54   0.43
8  2008-10-30  0.52   0.44
9  2008-11-02  0.53   0.44
10 2008-11-01  0.51   0.43
..        ...   ...    ...

\( f(x) = \mbox{E}(Y \mid X=x) \) is not a line.

ggplot(dat, aes(X, Y)) + geom_point(shape=1, cex=5) +
  geom_smooth(color="red")

sample_n(train_set,10) %>% select(label, pixel351:pixel358) %>% kable

\[ \mbox{dist}(1,2) = \sqrt{ \sum_{j=1}^{784} (Y_{1,j}-Y_{2,j })^2 } \]

\[ \mbox{dist}(15,273) = \sqrt{ \sum_{i=1}^{500} (Y_{i,15}-Y_{i,273})^2 } \]

X <- select(train_set , pixel0:pixel783) %>% as.matrix()

Rows and columns of matrices can be accessed like this:

thrid_row <- X[3,]
tenth_column <- X[,10]

X_1 <- X[1,]
X_2 <- X[2,]
X_253 <- X[253,]
sqrt(sum((X_1-X_2)^2))

[1] 2918.257

sqrt(sum((X_1-X_253)^2))

[1] 2787.913

d <- dist(X)
as.matrix(d)[1,2]

[1] 2918.257

as.matrix(d)[1,153]

[1] 3058.504

image(as.matrix(d))

Logistic regression is a straw man:

tmp_data <- select(train_set, y, X_1, X_2)
glm_fit <- glm(y~.,data = tmp_data )
f_hat <- predict(glm_fit, newdata = test_set, 
                 type = "response")
tab <- table(pred=round(f_hat), truth=test_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
   0.794 

knn_fit <- knn3(y~.,data = select(train_set, y, X_1, X_2) )
f_hat <- predict(knn_fit, newdata = test_set)[,2]
tab <- table(pred=round(f_hat), truth=test_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
   0.822 

f_hat <- predict(knn_fit, newdata = test_set)
tab <- table(pred=round(f_hat[,2]), 
             truth=test_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
   0.822 

f_hat_train <- predict(knn_fit, 
                       newdata = train_set)
tab <- table(pred=round(f_hat_train[,2]), 
             truth=train_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
   0.884 

Training set:

tmp_data <- select(train_set, y, X_1, X_2)
knn_fit_1 <- knn3(y~., data = tmp_data, k=1)
f_hat <- predict(knn_fit_1, 
                 newdata = train_set)
tab <- table(pred=round(f_hat[,2]), 
             truth=train_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
       1 

Test set:

f_hat <- predict(knn_fit_1,newdata =test_set)
tab <- table(pred=round(f_hat[,2]), 
             truth=test_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
    0.81 

knn_fit_251 <- knn3(y~.,data = select(train_set, y, X_1, X_2), k=251)
f_hat <- predict(knn_fit_251, newdata = test_set)[,2]
tab <- table(pred=round(f_hat), truth=test_set$y)
confusionMatrix(tab)$overall["Accuracy"]

Accuracy 
     0.8 

control <- trainControl(method='cv', number=2, p=.5)
dat2 <- mutate(dat, label=as.factor(label)) %>%
  select(label,X_1,X_2)
res <- train(label ~ .,
             data = dat2,
             method = "knn",
             trControl = control,
             tuneLength = 1, # How fine a mesh to go on grid
             tuneGrid=data.frame(k=seq(3,151,2)),
             metric="Accuracy")

Visualizing Results